Answer:
1 cupcake = $3.75
1 ice-cream = $4.50
1 doughnut = $1.50
Step-by-step explanation:
2 ice-cream + 1 cup cake = $12.75 ------------ [ 1 ]
1 ice-cream + 2 doughnuts = $7.50 ------------ [ 2 ]
1 cup cake + 1 doughnut + 1 ice-cream = $9.75 ------------ [ 3 ]
From [ 1 ] :
2 ice-cream + 1 cup cake = $12.75
1 cupcake = $12.75 - 2 ice-cream
Substitute [ 1 ] into [ 3 ]:
1 cup cake + 1 doughnut + 1 ice-cream = $9.75
$12.75 - 2 ice-cream + 1 doughnut + 1 ice-cream = $9.75
1 doughnut - 1 ice-cream = -$3 ------------ [ 4 ]
[ 2 ] + [ 4 ] :
3 doughnuts = $4.75
1 doughnut = $1.50
Substitute (1 doughnut = $1.50) into [ 2] :
1 ice-cream + 2 doughnuts = $7.50
1 ice-cream + 2 x $1.50 = $7.50
1 ice-cream + $3 = $7.50
1 ice-cream = $4.50
Substitute (1 ice-cream = $4.50) into [ 1 ]:
2 ice-cream + 1 cup cake = $12.75
2 x $4.50 + 1 cup cake = $12.75
1 cupcake = $12.75 - $9
1 cupcake = $3.75
To find the cost of each in a system of equations, you need to solve the equations simultaneously. You can solve for one variable first and substitute it into the other equation to find the value of the second variable. Once you have the value of one variable, you can substitute it back into one of the original equations to find the value of the other variable.
Explanation:In the field of Mathematics, specifically in algebra, a system of equations is a set of equations with the same variables. When you're asked to find the cost of each one, you're actually being asked to solve this system of equations. Let's assume your system of equations is:
5x + 2y = 40 (Equation 1) 3x + 4y = 35 (Equation 2)
You can solve for one variable first from either equation and substitute it into the other. For example, from Equation 1 you can solve for x: x = (40 - 2y)/5. Substituting x into Equation 2 gives us: 3((40 - 2y)/5) + 4y = 35. Solving this will give you the value of y which can then be substituted into any of the original equations to find the cost of x.
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find the surface area please. teacher checks soon
Answer:
Surface Area= 144
Step-by-step explanation:
To find the area of the triangle you would multiply the base times the height and divide it by 2. 9x6/2=27. For one triangle the area is 27. Since there are 4 you would multiply it by 4. 27x4= 108. This will give you 108. Now all you need to do is add the square which is 6x6= 36. 108+36=144.
Emily had 75 buttons. She gave 15 buttons to Jake. What percent of the buttons did Emily give to Jake?
20%
My equation:
15*100=1500
1500/75=20
The answer would be 20% off hope this helped!
Identify the features of the graph solution vertex y-intercept
Answer:
Vertex(3,-4) and y-int (0,5)
Zeroes are (1,0) and (5,0)
Step-by-step explanation:
Answer:
The solutions of the given graph are 1 and 5. The vertex of the graph is (3,-4) and the y-intercept of the graph is 5.
Step-by-step explanation:
From the given graph it is clear that it intersect the x-axis at (1,0) and (5,0).
Therefore the solutions of the given graph are 1 and 5.
Vertex of the parabola is the extreme point of the graph.
From the given graph it is clear that the the turning point or the extreme point of the graph is (3,-4).
Therefore the vertex of the graph is (3,-4).
The given graph intersect the y-axis at (0,5).
Therefore the y-intercept of the graph is 5.
ANSWER ASAP Which system of linear inequalities is represented by the graph
X+2y<4; 2y<-x+4; y<(-x/2)+2
Option 3
Find the slope of each line
Answer:
10
Step-by-step explanation:
You have to go up 10 places to get from the first point to the second
You also have to go 1 place to the right
Since the slope is Y/X, the slope of this line is 10/1
in triangle ABC the measure of A is 33° and the measure of C is 90° . what is the measure of B
Answer:
57°
Step-by-step explanation:
ALL angles in a triangle add up to 180°
SO, if we know the sum of two angles which is 123° (why: 33+90=123), all we have to do is subtract this number from 180 to get the measure of the 3rd angle. Which in this case is 57°
The measure of angle B will be 57° for the given triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right angle triangle, equilateral triangle, and much more.
The sum of all three interior angles of any triangle is 180°.
So,
A + B + C = 180°
Given,
A = 33° and C = 90°
33° + B + 90° = 180°
B = 180 - (90 + 33)
B = 180° - 123°
B = 57°
Hence, The measure of angle B will be 57° for the given triangle.
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Which equation is y=(x+3)^2 +(x+4)^2 rewritten in vertex form ?
Answer:
option B
Step-by-step explanation:
Given in the question an equation y = (x+3)² + (x+4)²
Step 1
Expand this equation
y = (x+3)² + (x+4)²
y = (x²+9+6x) + (x²+16+8x)
y = 2x² + 14x + 25
Step 2
Find the minimum point of the parabola equation, y = 2x² + 14x + 25
y = ax² + bx +c
x = -b/2a
= -14/2(2)
= -14/4
= -7/2
Step 3
Find the vertex point by plugging value of x in the equation
y = 2(-7/2)² + 14(-7/2) + 25
= 49/2 - 49 + 25
= 1/2
vertex (h,k)
vertex (-7/2 , 1/2)
Step 4
vertex form
y = a(x - h)²+ k
y = 2(x + 7/2)² + 1/2
help 10 points for correct answer asap
Answer:
Final answer is [tex]S_n=565.5[/tex].
Step-by-step explanation:
Given that [tex]a_1=12[/tex], [tex]a_n=75[/tex], and [tex]n=13[/tex].
Using those values, we need to find the value of [tex]S_n[/tex].
Plug these values into sum formula :
[tex]S_n=\frac{n}{2}\left(a_1+a_n\right)[/tex]
[tex]S_n=\frac{13}{2}\left(12+75\right)[/tex]
[tex]S_n=\frac{13}{2}\left(87\right)[/tex]
[tex]S_n=\frac{1}{2}\left(1131\right)[/tex]
[tex]S_n=565.5[/tex]
Hence final answer is [tex]S_n=565.5[/tex].
Hi will you plz telp me
Answer:
the mean is 73.4
Step-by-step explanation:
you add all the numbers which equals to 367
then divide by 5
What is the value of x in the solution to the system of equations below?
2x + y = 1
2x + 3y = 11
a.) x = - 2
b.) x = 3
c.) x = - 1
d.)x = 5
Answer:
A) X=-2
Step-by-step explanation:
by multiplying the first term by -3 then -6X-3y=-3
and 2X+3y=11
then by adding = -4X=8
then X=8/-4=-2
The value for x in the given system of equations is found by using the method of elimination, resulting in x = -2. The value of y was found first, namely y = 5, and was then substituted into the first equation to find x.
Explanation:The system of equations given is:
2x + y = 1 2x + 3y = 11To find the value of x, we can use the method of elimination or substitution. Let’s use elimination. First, subtract the first equation from the second.
That gives us: 2x + 3y - (2x + y) = 11 - 1
Which simplifies to: 2y = 10
Then divide both sides by 2: y = 5
Now substitute y = 5 into the first equation: 2x + 5 = 1, which simplifies to 2x = -4, and lastly x = -2.
So the solution for x in the system is x = -2 (option a.).
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What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters? 3.6 3,600,00 360 36
Answer: 3,600,000 cm³
Step-by-step explanation: First you have to convert all the units into centimeters,
2 meters = 200 centimeters
1.5 meters = 150 centimeters
To find the volume of a rectangular prism you multiply all the sides.
120 * 200 * 150 = 3,600,000
The answer is 3,600,000 cubic centimeters.
The volume of a rectangular prism with the given dimensions is 3.6 cubic meters.
The dimensions of a rectangular prism are 120 centimetres(1.2 meters) by 2 meters by 1.5 meters.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is l×b×h.
Now, volume=1.2×2×1.5=3.6 cubic meters.
Therefore, the volume of a rectangular prism is 3.6 cubic meters.
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Joel and Sara want to know the combined amount of money they made last week. They both made $9.75 per hour, but Joel also made an $18 bonus. Joel says the combined amount is 9.75j + 18 + 9.75s, where j is the number of hours he worked, and S is the number of hours Sara worked. Sara says the combined amount is 9.75(j + S)+ 18. Who is correct? Explain.
The would both be correct in it's own way depending on how the teacher is teaching.
Both Joel and Sara are correct. Their expressions represent the combined earnings accurately, considering hourly wage and bonus.
To determine who is correct, let's first break down the earnings for each person:
1. Joel:
- Hourly wage: $9.75
- Bonus: $18
Joel's total earnings can be calculated using the formula provided: [tex]\(9.75j + 18\)[/tex], where [tex]\(j\)[/tex] represents the number of hours Joel worked.
2. Sara:
- Hourly wage: $9.75
Sara's total earnings can be calculated using the formula provided: [tex]\(9.75(j + S)\)[/tex], where [tex]\(S\)[/tex] represents the number of hours Sara worked.
Now, let's expand both expressions and see which one correctly represents the combined earnings of Joel and Sara.
Joel's expression: [tex]\(9.75j + 18 + 9.75S\)[/tex]
Sara's expression: [tex]\(9.75j + 9.75S + 18\)[/tex]
Comparing the two expressions, we see that both expressions have the same terms: [tex]\(9.75j\)[/tex], [tex]\(9.75S\)[/tex], and [tex]\(18\)[/tex]. The order of terms is different, but mathematically it doesn't matter since addition is commutative.
So, both Joel and Sara are correct. They just wrote their expressions in a different order, but the mathematical result is the same. They both correctly accounted for their hourly wage and the bonus.
9. A new automobile costs $23,782,
but after one year it is worth
$17,668. What is the approximate
percent of decrease in the value of
the automobile?
Answer:
% decrease in the cost= 6114/23782⋅100=25.71%
Step-by-step explanation:
The decrease in the cost =$23782−$17668=$6114
Hence, % decrease in the cost=6114/23782⋅100=25.71%
the decrease is 23782 - 17668 = 6114.
if we take 23782 to be the 100%, what is 6114 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 23782&100\\ 6114&x \end{array}\implies \cfrac{23782}{6114}=\cfrac{100}{x}\implies 23782x=611400 \\\\\\ x=\cfrac{611400}{23782}\implies x\approx 25.71[/tex]
{29, 29, 29, 28, 28, 27}
What is the best measure of center for this data set?
a. mean because there is an outlier
b. mode because there is an outlier
c. median because there is an outlier
d. mean or median because there is no outlier
Please Help Me With This One :-/
So, you want to calculate the interest on $300 at 5% interest per year after 7 years.
The formula we'll use for this problem is:
I = P x r x tWhere:
P is the principal amount, $300.00r is the interest rate, 5% per year, or in decimal form, 5 / 100 = 0.05t is the time involved, 7 yearsTo find the simple interest, we multiply 300 x 0.05 x 7 to get that:
The interest is: $105.00
Answer:
The correct answer is last option
$105.00
Step-by-step explanation:
Points to remember
Simple interest
I = PNR/100
Where P - Principle amount
N - Number of years and
R - Rate of interest
To find the simple interest
Here P = $300, R = 5% and N = 7 years
I = PNR/100
= (300 * 5 * 7)/100
= 3 * 5 * 7
= 105
Therefore simple interest after 7 years = $105
The correct answer is last option
what is the slope of line that passes through the points (8, -9) and (14, -9)
Answer:
Step-by-step explanation:
[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{14}~,~\stackrel{y_2}{-9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-(-9)}{14-8}\implies \cfrac{-9+9}{6}\implies \cfrac{0}{6}\implies 0[/tex]
2) Jamie has twice as much money as Kristen. Together they have $36. How much money does each have?
Answer:
jamie has 24 and kristen is 12
Step-by-step explanation:
jamie is twice kristan which is 12+12
then 12 puls 24 is 36
For this case we have to:
Let x be the variable that represents the amount of money Jamie has.
Let y the variable that represents the amount of money that Kristen has
We have to:
[tex]x = 2y\\x + y = 36[/tex]
We substitute the first equation in the second:
[tex]2y + y = 36\\3y = 36\\y = \frac {36} {3}\\y = 12[/tex]
Looking for the value of x:
[tex]x = 2y\\x = 2 (12)\\x = 24[/tex]
Answer:
So, Jaime has $ 24 and Kristen has $ 12.
HURRY PLZ!!!
Solve for x: 1 x − 2 + 1 x + 2 = 4 x2 − 4
A) 0 B) 3 C) −1 D) no solution
Answer:
D) no solution
Step-by-step explanation:
1/ (x-2) + 1/(x+2) = 4/(x^2-4)
x cannot equal 2 or -2 since that would make our fractions equal 1/0 or be undefined
Factor the term on the right
1/ (x-2) + 1/(x+2) = 4/(x-2)(x+2)
Multiply both sides by (x-2) (x+2)
(x-2) (x+2) (1/ (x-2) + 1/(x+2)) = 4/(x-2)(x+2)*(x-2) (x+2)
Distribute
x+2 + (x-2) = 4
Combine like terms
2x = 4
Divide by 2
2x/2 = 4/2
x =2
But this is not a possible solution since that is not in the domain
what is 12x4 plz help
Answer:
it is 48 hope this helps
Step-by-step explanation:
The solution of expression is,
⇒ 48
We have to given that,
An expression to solve,
⇒ 12 × 4
Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Hence, We get;
⇒ 12 × 4
⇒ 48
Thus, The solution of expression is,
⇒ 48
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James found a pair of shoes he wanted at two stores. At store A they are $35 and he had a 20% off coupon. At store B they were $40 and he had a 30% off coupon. Which would be the better deal and by how much?
Answer: They cost the same amount.
Step-by-step explanation:
35(0.20)=7
35-7=28
40(0.30)=12
40-12=28
28=28
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is (x with a line over it), while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.
Confidence Level. 90%. 95%. 99%
z*-score. 1.645. 1.96. 2.58
Answer:
the answer is the (1.645 over root of n) on e 2020
Step-by-step explanation:
Answer:The answer is D
Step-by-step explanation: Hope this helps
Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, then what is the measure of angle CBD?
Answer choices:
a) 70 degrees
b) 120 degrees
c) 140 degrees
d) 40 degrees
Answer:b
Step-by-step explanation:
Zack buys some oranges from a store. The oranges cost $4.00 for 2 pounds. He wants to buy more fruit, but at the same price per pound as the oranges. Which of the following fruits could Zack buy?
A.
bananas at $2.00 for 5 pounds
B.
strawberries at $9.00 for 3 pounds
C.
peaches at $6.00 for 3 pounds
D.
blueberries at $8.00 for 2 pounds
Re
Answer:
C
Step-by-step explanation:
The oranges cost $4 per 2 lbs which is 4/2=$2 per lb. Option C has peaches at $6 for 3 lbs which is 6/3 =$2 per lb.
Answer:
C. Peaches at $6.00 Dollars for 3 pounds
Step-by-step explanation:
find the oranges $ per pound.
4 divided by 2 = 2
match it to each answer (example bellow, correct one)
6 divided by 3 = 2
Oranges per pound = $2.00
Peache per pound = $2.00
C.)
Hope this helped!
Lunar Rose Moon.
Juan has two machines: one exchanges 1 white token into 4 red tokens, while the other exchanges 1 red token into 3 white one. Juan has 4 white tokens. After exactly 11 exchanges , he has 31 tokens. How many of those are red?
Answer:
14 are red
Step-by-step explanation:
Let's identify the 2 types of transactions Juan machines do:
w : changes 1 white token into 4 red tokens (gain: 3 tokens overall)
r : changes 1 red token into 3 white tokens (gain: 2 tokens overall)
We know that Juan does 11 trades, so we can say:
w + r = 11
Overall, Juan started with 4 tokens and ends with 31... so, gain of 27 tokens.
We can model this as:
3w + 2r = 27
(3w because each w transaction, he gains 3 tokens, 2r because every r transaction, he gains 2 tokens).
From first equation we get r = 11 - w, which we place in the second equation:
3w + 2 (11 - w) = 27
3w + 22 - 2w = 27
w = 5, so r = 6 (from first equation).
Now, we know Juan did 5 w transactions and 6 r transactions. But how many token of each color does he have?
Start: 4W (4 White chips)
He does 4 w transactions, he now has 16R tokens
He does 6 r transactions, he now has 10 (16-6) R tokens, plus 18 W tokens
He does another w transaction, he now has 14 R (10 + 4), plus 17 W(18-1) tokens
He did 11 transactions, and he has 31 tokens at the end, out of which 14 are red.
A company needs 713 slices of pizza for a company party. If each pizza is cut into 8 slices, about how many whole pizzas should the company purchase. A) 60 B) 70 C) 80 D) 90
Answer: D
If there are 713 slices, and each pizza is divided into pieces, then you would divide.
713÷8=89.125. Round up and you get:
90.
Hope this helps and have a great day!!!
For this case we must indicate the number of whole pizzas needed for the company. For this we propose an equation.
Let "x" be the variable that represents the number of whole pizzas, then:
[tex]8x = 713[/tex]
We divide between 8 on both sides of the equation:
[tex]x = \frac {713} {8}\\x = 89,125[/tex]
90 pizzas are needed
ANswer:
Option D
look at the picture and plzz help me and also pick from the boxed sentences
The answers are:
3. Addition property of equality
4. [tex]6x-7+7=12+7[/tex] - Simplification
7. [tex]x=\frac{19}{6}[/tex]
Why?To solve the problem, we need to start with the result of the second step:
[tex]6x-7=12[/tex]
So,
For the step 3:
Then, for the 3rd step, we have to apply the addition property of equality.
The addition property of equality states that if we add a term to one side of the equality, we need to add it to the other side of the equality, in order to not alterate the equality.
Then, applying the property, we have:
[tex]6x-7=12[/tex]
Adding 7 to both sides, we have:
[tex]6x-7+7=12+7[/tex]
For the step 4:
Now, for the 4th step, we have to simplify the expression:
[tex]6x-7+7=12+7[/tex]
Then, simplifying, we have:
[tex]6x=19[/tex]
For the step 7:
Simplificating, we divide each side of the equality by 6:
[tex]\frac{6x}{6}=\frac{19}{6} \\\\x=\frac{19}{6}[/tex]
Have a nice day!
The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is
16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed
with the radius and the height of the cone.
(a) Sketch the roof of the castle tower. Label the known lengths as described and label the
unknown length as x.
(b) What is the slant height of the roof?
HOPE THIS WILL HELP YOU
Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).
A) y = 2x + 4
B) y = 2x - 8
C) y = -2x + 16
D) y = -1/2 + 7
will mark brainliest if correct and give 50 pts.
Answer:
The equation is y = - 1/2 x+7
Step-by-step explanation:
2 x + 4y = 6
4y = -2 x +6
Divide both sides by 4
y = - 1/2 x + 3/2
y=mx+b
slope m = - 1/2
The slope of a line parallel to another line will be the same
The slope of the required line will be - 1/2
m= - 1/2 ,point ( 6 , 4 )
Plugging the values of m and the point in
y=mx+b
4 = -3 + b
b= 7
m= - 1/2
Plug values y = mx +b
y = - 1/2 x+7
which values from the set{5,7,9,11,13} make the inequality w-4<8 true?
Answer:
5, 7, 9, 11
Step-by-step explanation:
Solve the inequality
w - 4 < 8 ( add 4 to both sides )
w < 12
w ∈ { 5, 7, 9, 11 }
find the total surface area of this cone. round to the nearest tenth(my last question of my homework and I keep getting it wrong)
Answer:
The surface area is approx. 1017.9 in^2.
Step-by-step explanation:
Total surface area of cone = πrl + πr^2. Since the radius is 12 in. and the slant height is 15 in, substitute 12 for r and 15 for l.
A = π(12)(15) + π(12)^2
= 180π + 144π
= 324π in^2
≈ 1017.9 in^2
Hope this helps!